Subgroups — #26220147

Order 12032.

1566 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13093958	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689124	C₂	1	2	yes	maximal, complemented
3	C₂×#15689078	C₂	1	1	yes	maximal, characteristic, complemented
4	#20245980	C₂	1	2	yes	maximal, complemented
5	#20244271	C₂	1	4	yes	maximal, complemented
6	#20244255	C₂	1	2	yes	maximal, complemented
7	#20244250	C₂	1	2	yes	maximal, complemented
8	C₂²×#135×C₄₇	C₂	1	1	yes	maximal, characteristic
9	C₂²×#10625329	C₂²	1	1	yes	characteristic
10	C₂×#13093983	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
12	C₂×#13093958	—	2	4	no	—
13	C₂×#13093958	C₂²	1	2	yes	—
14	C₂×#13093958	C₂²	1	2	yes	—
15	#15689124	—	2	8	no	—
16	C₂×#13093948	C₂²	1	4	yes	—
17	C₂×#13093945	C₂²	1	4	yes	—
18	#15689078	—	2	4	no	—
19	C₂×#13093934	C₂²	1	2	yes	—
20	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
21	#15689030	C₂²	1	4	yes	—
22	#15689026	C₂²	1	4	yes	—
23	#15689003	—	2	4	no	—
24	#15688983	—	2	4	no	—
25	C₂²×#41×C₄₇	C₂²	1	2	yes	—
26	C₂×#135×C₄₇	—	2	4	no	—
27	C₂×#135×C₄₇	—	2	4	no	—
28	C₂×#135×C₄₇	C₄	1	8	yes	complemented
29	C₂²×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
30	C₂²×SD₁₆×C₄₇	C₂²	1	2	yes	—
31	C₂²×D₈×C₄₇	C₂²	1	1	yes	characteristic
32	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
33	C₂³×Dic₄₇	—	2	2	no	—
34	C₂×#10625329	—	2	2	no	—
35	C₂×#10625329	—	2	2	no	—
36	C₂×#10625329	D₄	1	4	yes	—
37	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
38	#13093983	—	2	2	no	—
39	#13093983	—	2	2	no	—
40	C₂×C₄⋊Dic₄₇	—	2	4	no	—
41	C₂×C₄⋊Dic₄₇	—	2	4	no	—
42	C₂×C₄⋊Dic₄₇	—	2	2	no	—
43	C₂×C₄⋊Dic₄₇	D₄	1	2	yes	—
44	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
45	C₂×C₂²⋊Dic₄₇	—	2	8	no	—
46	C₂×C₂²⋊Dic₄₇	D₄	1	2	yes	—
47	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
48	#13093958	—	2	4	no	—
49	#13093958	—	2	4	no	—
50	#13093948	—	2	8	no	—
51	#13093945	—	2	8	no	—
52	#13093934	—	2	4	no	—
53	C₈×Dic₄₇	—	2	4	no	—
54	C₄₇⋊#95	—	2	8	no	—
55	C₂×#41×C₄₇	—	2	4	no	—
56	C₂×#41×C₄₇	—	2	4	no	—
57	C₂×#41×C₄₇	—	2	4	no	—
58	C₂×#41×C₄₇	—	2	4	no	—
59	C₂×#41×C₄₇	—	2	4	no	—
60	C₂×#41×C₄₇	C₂×C₄	1	8	yes	—
61	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
62	C₂²×D₄×C₄₇	—	2	2	no	—
63	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
64	C₂³×C₄×C₄₇	—	2	2	no	—
65	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
66	#135×C₄₇	—	2	32	no	—
67	C₂×Q₁₆×C₄₇	—	2	2	no	—
68	C₂×Q₁₆×C₄₇	—	2	2	no	—
69	C₂×Q₁₆×C₄₇	C₂×C₄	1	4	yes	complemented
70	C₂×SD₁₆×C₄₇	—	2	4	no	—
71	C₂×SD₁₆×C₄₇	—	2	4	no	—
72	C₂×SD₁₆×C₄₇	C₂×C₄	1	8	yes	complemented
73	C₂×D₈×C₄₇	—	2	2	no	—
74	C₂×D₈×C₄₇	—	2	2	no	—
75	C₂×D₈×C₄₇	C₂×C₄	1	4	yes	complemented
76	C₂²×C₈×C₄₇	C₂×C₄	1	4	yes	—
77	C₂²×C₈×C₄₇	D₄	1	4	yes	—
78	C₂²×C₈×C₄₇	D₄	1	4	yes	—
79	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
81	C₂⁴×C₄₇	—	2	2	no	—
82	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
83	#41×C₄₇	—	2	16	no	—
84	#41×C₄₇	—	2	16	no	—
85	#41×C₄₇	—	4	8	no	—
86	#41×C₄₇	—	4	8	no	—
87	C₂×Q₈×C₄₇	—	2	2	no	—
88	C₂×Q₈×C₄₇	—	2	2	no	—
89	C₂×Q₈×C₄₇	—	2	2	no	—
90	C₂×Q₈×C₄₇	—	2	2	no	—
91	C₂×Q₈×C₄₇	—	2	2	no	—
92	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
93	C₂×D₄×C₄₇	—	2	8	no	—
94	C₂×D₄×C₄₇	—	2	2	no	—
95	C₂×D₄×C₄₇	—	2	2	no	—
96	C₂×D₄×C₄₇	—	2	2	no	—
97	C₂×D₄×C₄₇	—	2	2	no	—
98	C₂×D₄×C₄₇	—	2	2	no	—
99	C₂×D₄×C₄₇	—	4	4	no	—
100	C₂×D₄×C₄₇	—	4	4	no	—
101	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
102	C₂²×C₄×C₄₇	—	2	2	no	—
103	C₂²×C₄×C₄₇	—	2	8	no	—
104	C₂²×C₄×C₄₇	—	4	4	no	—
105	C₂²×C₄×C₄₇	—	4	4	no	—
106	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₄₇	#41	1	2	yes	—
112	C₂²×C₄×C₄₇	#41	1	2	yes	—
113	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
114	C₂²×Dic₄₇	—	2	4	no	—
115	C₂²×Dic₄₇	—	4	4	no	—
116	C₂²×Dic₄₇	—	8	4	no	—
117	C₂²×Dic₄₇	C₂×D₄	1	4	yes	—
118	Q₁₆×C₄₇	—	2	8	no	—
119	SD₁₆×C₄₇	—	2	16	no	—
120	D₈×C₄₇	—	2	8	no	—
121	C₂×C₈×C₄₇	C₂²⋊C₄	1	16	yes	complemented
122	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
123	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
124	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
125	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
126	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
127	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
128	C₂²⋊Dic₄₇	—	2	4	no	—
129	C₂²⋊Dic₄₇	—	8	8	no	—
130	C₄⋊Dic₄₇	—	2	4	no	—
131	C₄⋊Dic₄₇	—	2	4	no	—
132	C₄⋊Dic₄₇	—	2	4	no	—
133	C₄⋊Dic₄₇	—	4	4	no	—
134	C₄×Dic₄₇	—	2	2	no	—
135	C₄×Dic₄₇	—	2	2	no	—
136	#10625329	—	2	8	no	—
137	C₂×C₄₇⋊C₈	—	2	2	no	—
138	C₂×C₄₇⋊C₈	—	2	2	no	—
139	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
140	C₂³×C₄₇	—	2	2	no	—
141	C₂³×C₄₇	—	2	2	no	—
142	C₂³×C₄₇	—	2	4	no	—
143	C₂³×C₄₇	—	4	2	no	—
144	C₂³×C₄₇	—	4	2	no	—
145	C₂³×C₄₇	—	4	4	no	—
146	C₂³×C₄₇	—	4	4	no	—
147	C₂³×C₄₇	C₄×D₄	1	2	yes	—
148	C₂³×C₄₇	#121	1	2	yes	—
149	C₂³×C₄₇	#127	1	2	yes	—
150	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
151	Q₈×C₄₇	—	2	4	no	—
152	Q₈×C₄₇	—	2	4	no	—
153	Q₈×C₄₇	—	4	2	no	—
154	Q₈×C₄₇	—	4	2	no	—
155	D₄×C₄₇	—	2	4	no	—
156	D₄×C₄₇	—	2	4	no	—
157	D₄×C₄₇	—	4	16	no	—
158	D₄×C₄₇	—	4	2	no	—
159	D₄×C₄₇	—	4	2	no	—
160	C₂×C₄×C₄₇	—	2	4	no	—
161	C₂×C₄×C₄₇	—	4	2	no	—
162	C₂×C₄×C₄₇	—	4	2	no	—
163	C₂×C₄×C₄₇	—	4	16	no	—
164	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
165	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
166	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
167	C₂×C₄×C₄₇	#121	1	4	yes	—
168	C₂×C₄×C₄₇	#121	1	2	yes	—
169	C₂×C₄×C₄₇	#124	1	4	yes	—
170	C₂×C₄×C₄₇	#127	1	2	yes	—
171	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
176	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
177	C₂×Dic₄₇	—	2	4	no	—
178	C₂×Dic₄₇	—	2	4	no	—
179	C₂×Dic₄₇	—	2	4	no	—
180	C₂×Dic₄₇	—	4	4	no	—
181	C₂×Dic₄₇	—	4	8	no	—
182	C₂×Dic₄₇	—	8	8	no	—
183	C₈×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
184	C₈×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
185	C₄₇⋊C₈	—	2	4	no	—
186	#21230	—	47	1	no	maximal, Sylow
187	C₂²×C₄₇	—	2	2	no	—
188	C₂²×C₄₇	—	2	2	no	—
189	C₂²×C₄₇	—	2	4	no	—
190	C₂²×C₄₇	—	2	4	no	—
191	C₂²×C₄₇	—	4	8	no	—
192	C₂²×C₄₇	—	4	4	no	—
193	C₂²×C₄₇	—	8	2	no	—
194	C₂²×C₄₇	—	8	2	no	—
195	C₂²×C₄₇	—	8	4	no	—
196	C₂²×C₄₇	#390	1	4	yes	—
197	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
198	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
199	C₂²×C₄₇	C₂×#127	1	1	yes	characteristic
200	C₂²×C₄₇	#576	1	2	yes	—
201	C₂²×C₄₇	#578	1	2	yes	—
202	C₄×C₄₇	—	4	4	no	—
203	C₄×C₄₇	#390	1	4	yes	—
204	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
205	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
206	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
207	C₄×C₄₇	C₂×#124	1	1	yes	characteristic
208	Dic₄₇	—	4	4	no	—
209	Dic₄₇	—	8	4	no	—
210	C₂²×#135	D₄₇	1	1	yes	characteristic
211	C₂²×#107	—	47	1	no	—
212	C₂×#417	—	47	2	no	—
213	C₂×#405	—	47	1	no	—
214	#2311	—	47	2	no	—
215	#1973	—	47	4	no	—
216	#1970	—	47	2	no	—
217	#1969	—	47	2	no	—
218	C₂×C₄₇	—	2	4	no	—
219	C₂×C₄₇	—	8	4	no	—
220	C₂×C₄₇	C₂×#390	1	1	yes	characteristic
221	C₂×C₄₇	#2951	1	2	yes	—
222	C₂×C₄₇	#3061	1	2	yes	—
223	C₂×C₄₇	#3155	1	1	yes	characteristic
224	C₂×C₄₇	#3156	1	1	yes	characteristic
225	C₂²×#41	C₂×D₄₇	1	2	yes	—
226	C₂×#135	—	2	4	no	—
227	C₂×#135	—	2	4	no	—
228	C₂×#135	Dic₄₇	1	8	yes	complemented
229	C₂²×Q₁₆	C₂×D₄₇	1	1	yes	characteristic
230	C₂²×SD₁₆	C₂×D₄₇	1	2	yes	—
231	C₂²×D₈	C₂×D₄₇	1	1	yes	characteristic
232	C₂²×M₁₆	—	47	1	no	—
233	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
234	C₂×#117	—	47	1	no	—
235	C₂²×C₄⋊C₄	—	47	2	no	—
236	C₂×#107	—	47	2	no	—
237	C₂×#107	—	47	2	no	—
238	C₂×#107	—	94	4	no	—
239	#417	—	94	8	no	—
240	C₂×#103	—	47	4	no	—
241	C₂×#102	—	47	4	no	—
242	#405	—	94	4	no	—
243	C₂×#97	—	47	2	no	—
244	C₂×C₄×C₈	—	47	2	no	—
245	#391	—	47	4	no	—
246	#390	—	47	4	no	—
247	#386	—	94	4	no	—
248	#380	—	94	4	no	—
249	C₄₇	#21230	1	1	yes	characteristic, complemented, Sylow
250	C₂×#41	—	2	4	no	—
251	C₂×#41	—	2	4	no	—
252	C₂×#41	—	2	4	no	—
253	C₂×#41	—	2	4	no	—
254	C₂×#41	—	2	4	no	—
255	C₂×#41	C₂×Dic₄₇	1	8	yes	—
256	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
257	C₂²×D₄	—	2	2	no	—
258	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
259	C₂³×C₄	—	2	2	no	—
260	C₂³×C₄	—	94	2	no	—
261	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
262	#135	—	2	32	no	—
263	C₂×Q₁₆	—	2	2	no	—
264	C₂×Q₁₆	—	2	2	no	—
265	C₂×Q₁₆	C₂×Dic₄₇	1	4	yes	complemented
266	C₂×SD₁₆	—	2	4	no	—
267	C₂×SD₁₆	—	2	4	no	—
268	C₂×SD₁₆	C₂×Dic₄₇	1	8	yes	complemented
269	C₂×D₈	—	2	2	no	—
270	C₂×D₈	—	2	2	no	—
271	C₂×D₈	C₂×Dic₄₇	1	4	yes	complemented
272	C₂×M₁₆	—	47	4	no	—
273	C₂×M₁₆	—	94	2	no	—
274	C₂×M₁₆	—	94	2	no	—
275	C₂²×C₈	—	47	2	no	—
276	C₂²×C₈	C₂×Dic₄₇	1	4	yes	—
277	C₂²×C₈	C₂²⋊D₄₇	1	4	yes	—
278	C₂²×C₈	C₂²⋊D₄₇	1	4	yes	—
279	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
280	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
281	#117	—	94	2	no	—
282	#117	—	94	2	no	—
283	C₂×C₄⋊C₄	—	47	2	no	—
284	C₂×C₄⋊C₄	—	47	4	no	—
285	C₂×C₄⋊C₄	—	94	4	no	—
286	C₂×C₄⋊C₄	—	94	4	no	—
287	C₂×C₄⋊C₄	—	94	2	no	—
288	C₂×C₂²⋊C₄	—	47	2	no	—
289	C₂×C₂²⋊C₄	—	94	8	no	—
290	C₂×C₄²	—	47	2	no	—
291	#107	—	94	4	no	—
292	#107	—	94	4	no	—
293	#103	—	94	8	no	—
294	#102	—	94	8	no	—
295	#97	—	94	4	no	—
296	C₄×C₈	—	94	4	no	—
297	#95	—	94	8	no	—
298	C₂⁴	—	2	2	no	—
299	C₂⁴	D₄×D₄₇	1	1	yes	characteristic
300	#41	—	2	16	no	—
301	#41	—	2	16	no	—
302	#41	—	4	8	no	—
303	#41	—	4	8	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	—	2	2	no	—
306	C₂×Q₈	—	2	2	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	—	2	2	no	—
309	C₂×Q₈	C₂²×Dic₄₇	1	4	yes	—
310	C₂×D₄	—	2	8	no	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	—	2	2	no	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	—	4	4	no	—
317	C₂×D₄	—	4	4	no	—
318	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	8	no	—
321	C₂²×C₄	—	4	4	no	—
322	C₂²×C₄	—	4	4	no	—
323	C₂²×C₄	—	47	4	no	—
324	C₂²×C₄	—	94	4	no	—
325	C₂²×C₄	—	376	4	no	—
326	C₂²×C₄	—	188	4	no	—
327	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
328	C₂²×C₄	D₄×D₄₇	1	2	yes	—
329	C₂²×C₄	#10625352	1	2	yes	—
330	C₂²×C₄	#10625352	1	2	yes	—
331	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
332	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
333	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
334	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
335	Q₁₆	—	2	8	no	—
336	SD₁₆	—	2	16	no	—
337	D₈	—	2	8	no	—
338	M₁₆	—	94	8	no	—
339	C₂×C₈	—	47	4	no	—
340	C₂×C₈	—	94	2	no	—
341	C₂×C₈	—	94	2	no	—
342	C₂×C₈	C₂²⋊Dic₄₇	1	16	yes	complemented
343	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
344	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
345	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
346	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
347	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
348	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
349	C₄⋊C₄	—	94	4	no	—
350	C₄⋊C₄	—	94	4	no	—
351	C₄⋊C₄	—	94	4	no	—
352	C₄⋊C₄	—	188	4	no	—
353	C₂²⋊C₄	—	94	4	no	—
354	C₂²⋊C₄	—	376	8	no	—
355	C₄²	—	94	2	no	—
356	C₄²	—	94	2	no	—
357	C₂³	—	2	2	no	—
358	C₂³	—	2	2	no	—
359	C₂³	—	2	4	no	—
360	C₂³	—	4	2	no	—
361	C₂³	—	4	2	no	—
362	C₂³	—	4	4	no	—
363	C₂³	—	4	4	no	—
364	C₂³	D₄×Dic₄₇	1	2	yes	—
365	C₂³	#13093995	1	2	yes	—
366	C₂³	#13094020	1	2	yes	—
367	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
368	Q₈	—	2	4	no	—
369	Q₈	—	2	4	no	—
370	Q₈	—	4	2	no	—
371	Q₈	—	4	2	no	—
372	D₄	—	2	4	no	—
373	D₄	—	2	4	no	—
374	D₄	—	4	16	no	—
375	D₄	—	4	2	no	—
376	D₄	—	4	2	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	16	no	—
381	C₂×C₄	—	94	4	no	—
382	C₂×C₄	—	94	4	no	—
383	C₂×C₄	—	94	4	no	—
384	C₂×C₄	—	376	8	no	—
385	C₂×C₄	—	188	4	no	—
386	C₂×C₄	—	188	8	no	—
387	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
388	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
389	C₂×C₄	D₄×Dic₄₇	1	4	yes	—
390	C₂×C₄	#13093995	1	2	yes	—
391	C₂×C₄	#13093995	1	4	yes	—
392	C₂×C₄	#13094011	1	4	yes	—
393	C₂×C₄	#13094020	1	2	yes	—
394	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
395	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
396	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
397	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
398	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
399	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
400	C₈	—	94	4	no	—
401	C₈	C₂×C₂²⋊Dic₄₇	1	4	yes	—
402	C₈	C₂×C₂²⋊Dic₄₇	1	4	yes	—
403	C₂²	—	2	4	no	—
404	C₂²	—	2	4	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	2	2	no	—
407	C₂²	—	4	4	no	—
408	C₂²	—	4	8	no	—
409	C₂²	—	8	4	no	—
410	C₂²	—	8	2	no	—
411	C₂²	—	8	2	no	—
412	C₂²	#15689026	1	4	yes	—
413	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
414	C₂²	C₂×#13093995	1	1	yes	characteristic
415	C₂²	C₂×#13094020	1	1	yes	characteristic
416	C₂²	#15689925	1	2	yes	—
417	C₂²	#15689937	1	2	yes	—
418	C₄	—	4	4	no	—
419	C₄	—	376	4	no	—
420	C₄	—	188	4	no	—
421	C₄	#15689026	1	4	yes	—
422	C₄	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
423	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
424	C₄	C₂×#13093995	1	1	yes	characteristic
425	C₄	C₂×#13094011	1	1	yes	characteristic
426	C₂	—	2	4	no	—
427	C₂	—	8	4	no	—
428	C₂	C₂×#15689026	1	1	yes	characteristic
429	C₂	#20252264	1	2	yes	—
430	C₂	#20253054	1	2	yes	—
431	C₂	#20253875	1	1	yes	characteristic
432	C₂	#20253883	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting, prime radical	C₂²×#135×C₄₇	C₂
socle	C₂³×C₄₇	C₂²×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂²×#135	D₄₇
hypocenter	C₄₇	#21230
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂²×#135

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂²×#13093958	C₂	semidirect
2. C₂×#15689124	C₂	semidirect
3. C₂×#15689078	C₂	semidirect
4. #20245980	C₂	semidirect
5. #20244271	C₂	semidirect
6. #20244255	C₂	semidirect
7. #20244250	C₂	semidirect
28. C₂×#135×C₄₇	C₄	semidirect
69. C₂×Q₁₆×C₄₇	C₂×C₄	semidirect
72. C₂×SD₁₆×C₄₇	C₂×C₄	semidirect
75. C₂×D₈×C₄₇	C₂×C₄	semidirect
121. C₂×C₈×C₄₇	C₂²⋊C₄	semidirect
228. C₂×#135	Dic₄₇	semidirect
249. C₄₇	#21230	semidirect
265. C₂×Q₁₆	C₂×Dic₄₇	semidirect
268. C₂×SD₁₆	C₂×Dic₄₇	semidirect
271. C₂×D₈	C₂×Dic₄₇	semidirect
342. C₂×C₈	C₂²⋊Dic₄₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×#13093958	2
C₂×#15689124	2
C₂×#15689078	2
#20245980	2
#20244271	2
#20244255	2
#20244250	2
C₂²×#135×C₄₇	2
#21230	47